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A054799 Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n. 18
3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 434, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Only 3 composite numbers are known: 434, 8575, 8825. This sequence is the union of A050507 and A001359.
The terms are also the solutions of A001065(x) = A001065(x+2), where A001065(n) is the sum of proper divisors of n. - Michel Marcus, Nov 14 2014
REFERENCES
Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81.
LINKS
EXAMPLE
n = 434, divisors = {1, 2, 7, 14, 31, 62, 217, 434}, sigma(434) = 768, sigma(436) = 770; n = 8575, divisors = {1, 5, 7, 25, 35, 49, 175, 245, 343, 1225, 1715, 8575}, sigma(8575) = 12400, sigma(8577) = 12402; n = 8825, divisors = {1, 5, 25, 353, 1765, 8825}, sigma(8525) = 10974, sigma(8527) = 10976.
MATHEMATICA
Select[Range[1500], DivisorSigma[1, #+2]==DivisorSigma[1, #]+2&] (* Jayanta Basu, May 01 2013 *)
PROG
(PARI) is(n)=sigma(n+2)==sigma(n)+2 \\ Charles R Greathouse IV, Feb 13 2013
CROSSREFS
Sequence in context: A329946 A063700 A078859 * A093326 A001359 A096292
KEYWORD
nonn
AUTHOR
Labos Elemer, May 22 2000
STATUS
approved

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Last modified May 18 15:19 EDT 2024. Contains 372662 sequences. (Running on oeis4.)